Pith Number

pith:FDHQ5IS2

pith:2021:FDHQ5IS2IFBFP7FC4DKBN5XBET

not attested not anchored not stored refs pending

Quasinormal Modes of Black Holes with Multiple Photon Spheres

Guangzhou Guo, Haitang Yang, Houwen Wu, Peng Wang

arxiv:2112.14133 v2 · 2021-12-28 · gr-qc · hep-th

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FDHQ5IS2IFBFP7FC4DKBN5XBET}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Strong-deflection expansion of the deflection angle near a degenerate photon sphere

Receipt and verification

First computed	2026-07-05T04:35:41.284419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28cf0ea25a414257fca2e0d416f6e124eacc23ad2344395393054b4504bcd45a

Aliases

arxiv: 2112.14133 · arxiv_version: 2112.14133v2 · doi: 10.48550/arxiv.2112.14133 · pith_short_12: FDHQ5IS2IFBF · pith_short_16: FDHQ5IS2IFBFP7FC · pith_short_8: FDHQ5IS2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 28cf0ea25a414257fca2e0d416f6e124eacc23ad2344395393054b4504bcd45a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c6b362dd347ba754feba2a36fd518747a203ac8e54ca1286851dbfcf41a542d",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-12-28T13:22:20Z",
    "title_canon_sha256": "530826e40b5351ca6e2dbb22dd89a3c78d5f62843644ba1693b269d8ba7c2eac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.14133",
    "kind": "arxiv",
    "version": 2
  }
}